Some digital communication systems use equalization to increase accurate detection of transmitted symbols in the presence of intersymbol interference (ISI). Equalization can be used to compensate for this ISI so that the transmitted symbols are accurately detected. Such equalization systems are well known (see for example, U.S. Pat. Nos. 5,414,734 and 5,513,15 for a discussion of equalization). FIG. 1 is a simplified diagram illustrative of a system 10 that uses equalization.
System 10 includes a transmitter 12, a receiver 14 with an equalizer 16. In this example, system 10 is a mobile wireless digital system in which transmitter 12 broadcasts radiofrequency (RF) signals that are modulated to include digital information. In this system, transmitter 12 receives symbols x(t), which transmitter 12 modulates and broadcasts. Each symbol generally represents one or more bits. For example, each symbol of a sixteen-level quadrature amplitude modulation (QAM) scheme represents four bits.
The broadcasted symbol is propagated through a channel 18, which is indicated by a dashed box in FIG. 1. Receiver 14 then receives the broadcasted symbol. Although omitted from FIG. 1 for clarity, in system 10 receiver 14 generally receives a transmission through more than one transmission path. For example, the multiple paths may be the result of more than one transmitter being used to transmit the signals and/or the transmitted signal from a single transmitter being reflected from nearby structures. Typically, the transmission paths between receiver 14 and the various other transmitters are not equal in length and may be changing over time (due to receiver 14 being moved while receiving a symbol), thereby resulting in multipath fading and ISI. Channel 18 represents the multiple paths and can include effects from the transmitter and receiver (e.g., pulse shaping filters, modulation inaccuracies, etc.). Typically, channel 18 is modeled as a time-variant finite impulse response (FIR) filter.
Equalizer 16 compensates for ISI as the ISI changes over time. This compensation allows receiver 14 to more accurately detect the received symbols. The compensation provided by equalizer 16 can be adjusted during operation based on periodically generated estimates of the channel response where the channel is modeled as in system 10.
FIG. 2 is a simplified functional block diagram illustrative of conventional exemplary equalizer 16 (FIG. 1). Equalizer 16 includes a decision feedback equalizer circuit (DFE) 22, a channel estimator 24 and a channel interpolator 26. For example, U.S. Pat. No. 5,513,215 discloses an estimator with a DFE, channel estimator and channel interpolator. The basic operation of exemplary equalizer 16 is as follows. Symbol samples are received by receiver 14 (FIG. 1) and propagated to DFE 22 and channel estimator 24. Channel estimator 24 and channel interpolator 26 operate to periodically provide, in effect, a highly "defined" estimate of the response of channel 18. This interpolated estimate of the channel response allows computation of the coefficients of DFE 22 so that DFE 22 can accurately detect the received symbols.
More specifically, channel estimator 24 uses known pilot symbols that are periodically inserted in the transmitted data sequence. The rate at which the pilot symbols are inserted is related to the highest fading rate that channel estimator 24 can follow. In particular, the frequency of the pilot symbol injection is about two or more times the fading rate that the channel estimator 24 can track (i.e., meeting Nyquist rate constraints). For example, a paging system application adapted for use in a fading environment with a fading rate of about 100 Hz, the pilot symbol insertion rate may be set at about 360 Hz.
Channel interpolator 26 uses the channel estimates from channel estimator 24 to compute the interpolated channel estimates to match the frequency of the received symbols transmitted by transmitter 12 (FIG. 1), or with a higher frequency than the symbol frequency if the receiver uses oversampling techniques. In the aforementioned paging system application, the symbol rate may be about 18 kHz. Thus, the 360 Hz pilot symbol insertion rate requires that channel interpolator 26 interpolate the channel estimates on the order of fifty times. In such cases, high-order interpolators (i.e., fifty or greater) are typically implemented with multistage interpolators to reduce computational load.
FIG. 3 is a block diagram illustrative of multistage channel interpolator 26 (FIG. 2). To get any order of interpolation and a linear phase response of the interpolator, channel interpolator 26 is conventionally implemented using a zero-stuffing technique with filtering through several FIR filter stages 31.sub.1 -31.sub.j and applying a linear interpolator 53 at the end as a last stage. Linear interpolator 53 is able to implement even the noninteger interpolation values. It can be used as the final stage of interpolation because the earlier FIR filter stages 31.sub.1 -31.sub.j interpolate the estimated impulse response to well above the Nyquist rate of channel estimator 24, which is determined by the pilot symbol insertion rate. In addition, because the channel fading process is sampled so that the Nyquist rate is close to the fading rate, the first FIR filter stage 31.sub.1 generally must have a relatively narrow transition bandwidth to filter out noise and prevent aliasing. However, to achieve a narrow transition bandwidth in an FIR filter, a relatively large number of coefficients is required. The large number of coefficients undesirably incurs a relatively large computational load and a relatively large initial filter delay. Accordingly, there is a need for a channel interpolator that has a first stage that provides a narrow transition bandwidth with a linear phase response with fewer filter coefficients.